The cases where both the strength characteristics and the load characteristics vary in time
require special consideration and will be shortly discussed in the following.
In cases where the strength characteristics are slowly deteriorating and the loading
characteristics vary in time the reliability assessment problem in principle must be addressed
as a first passage problem as discussed in the foregoing section. The situation is illustrated in
Figure 8.5.
Resistance and loadTime
TX(t)b(t)Figure 8.5: Illustration of the time variant problem with slowly time varying strength characteristics.
In cases where the strength characteristics are deteriorating very fast it may be sufficiently
accurate to approximate the time varying problem by a time in-variant problem where the load
process is represented by its extreme value distribution corresponding to a time interval,
which is representative for the time instance where the strength characteristics are reduced the
most. The situation is illustrated in Figure 8.6.
Resistance and loadTime
TX(t)b(t)Figure 8.6: Illustration of the time variant problem with rapidly time varying strength characteristics.
In e.g. fatigue crack growth problems it is in some cases sufficiently accurate to assess the
failure probability for the service life [0;T] by using the strength characteristics corresponding
to time T, i.e. the lowest value in the considered time interval, and the annual extreme value
distribution of the load.